Question
In: Operations Management
The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires...
The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires 8 hours to produce one lot o shag carpet and 6 hours to produce one lot of sculpture carpet. The company has the following production goals, in prioritized order:
1) Do Not underutilize production capacity, which is 480 hours.
2) Achieve product demand for shag is more important than meeting demand for sculptured, by a ration of 5 to 2.
3) Limit production overtime to 20 hours
Solve:
a) Fromulate a Goal Programming Model to determine teh amount of shag and sculptured carpet to produce the best meet the company's goals.
b) Solve his model by using the computer (Excel and Solver)
Please help solve this. Use Excel to set up the table and utilize solver. I need help with that part and explaining. Thank you.
Solutions
Expert Solution
(a)
Let X1 and X2 be the number of lots of shag and sculpture carpets to be produced respectively. Also, Let Ui and Oi be the under and overachievements of the i-th goal.
Objective function: Minimize Z = 3*U1 + 2*(5/7)*U2 + 2*(2/7)*U3
+ 1*O1
Subject to,
8X1 + 6X2 + U1 - O1 = 480 (min labor hours - goal 1)
X1 + U2 - O2 = 40 (demand for X1 - goal 2)
X2 + U3 - O3 = 50 (demand for X2 - goal 2)
8X1 + 6X2 + U1 - O1 = 480 (max labor hours - goal 3)
X1, X2, Ui, Oi >= 0
----------------------------
(b)
keosha answered 1 year agoRelated Solutions
Question: The Wearever Carpet Company manufactures two brands of carpet, shag and sculptured, in 100-yard lots....
Question:
The Wearever Carpet Company manufactures two brands of carpet,
shag and sculptured, in 100-yard lots. It requires eight hours to
produce one lot of shag carpet and six hours to produce one lot of
sculptured carpet. The company has the following production goals
in prioritized order.
(1) Do not underutilize production capacity, which is 480
hours.
(2) Limit production overtime to 20 hours.
(3) Achieve product demand of forty 100-yard lots for shag and
fifty 100-yard lots for sculptured...
10. The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured—in 10-yard lots. It requires...
10. The Wearever Carpet Company manufactures two brands
of carpet—shag and sculptured—in 10-yard lots. It requires 8 hours
to produce one lot of shag carpet and 6 hours to produce one lot of
sculptured carpet. The company has the following production goals,
in prioritized order:
(1) Do not underutilize production capacity, which is
480 hours.
(2) Achieve product demand of 40 (100-yard) lots for
shag and 50 (100-yard) lots for sculptured carpet. Meeting demand
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added at the beginning of the process and the process is completed.
On January 1, Port Ormond Carpet Company had the following
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FloorMate Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On October 1, FloorMate
Carpet Company had the following inventories:
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FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it...
FloorMate Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On October 1, FloorMate
Carpet Company had the following inventories:
Finished Goods
$8,300
Work in Process-Spinning
Department
2,000
Work in Process-Tufting
Department
2,600
Materials
4,800
Departmental accounts are maintained for factory overhead,...
FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it...
FloorMate Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On October 1, FloorMate
Carpet Company had the following inventories:
Finished Goods
$6,200
Work in Process-Spinning
Department
1,100
Work in Process-Tufting
Department
2,700
Materials
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Departmental accounts are maintained for factory overhead,...
FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it...
FloorMate Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On October 1, FloorMate
Carpet Company had the following inventories:
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$7,200
Work in Process-Spinning
Department
1,000
Work in Process-Tufting
Department
2,400
Materials
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Departmental accounts are maintained for factory overhead,...
Port Ormond Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where...
Port Ormond Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On January 1, Port Ormond
Carpet Company had the following inventories:
Finished Goods
$62,000
Work in
Process-Spinning Department
35,000
Work in
Process-Tufting Department
28,500
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17,000
Departmental accounts are maintained for...
Port Ormond Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where...
Port Ormond Carpet Company manufactures carpets. Fiber is placed
in process in the Spinning Department, where it is spun into yarn.
The output of the Spinning Department is transferred to the Tufting
Department, where carpet backing is added at the beginning of the
process and the process is completed. On January 1, Port Ormond
Carpet Company had the following inventories:
Finished Goods
$6,200
Work in Process-Spinning Department
1,100
Work in Process-Tufting Department
2,700
Materials
4,200
Departmental accounts are maintained for...
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